1. Field of the Invention
The present invention relates to signal processing, and more specifically, to demapping of received data symbols.
2. Description of the Related Art
Overview of Prior-Art OFDM Transmitter and Receiver
FIG. 1 shows a simplified block diagram of one possible implementation of a prior-art OFDM transmitter 100. Transmitter 100 converts digital data into analog OFDM signals for transmission. Conversion occurs through steps of processing beginning with upstream processing 102. Upstream processing 102 performs operations to generate a serial bitstream of digital data and might include processing such as convolution coding, analog-to-digital conversion, or other processing.
Data symbol mapper 104 divides the serial bitstream into groups of bits, where each group is mapped into a separate data symbol C[k] using any one of a number of mapping techniques commonly known in the art, including but not limited to quadrature phase-shift keying (QPSK) and 16-quadrature amplitude modulation (16-QAM).
Inverse fast Fourier transform (IFFT) processor 106 performs OFDM modulation to convert the data symbols into OFDM symbols. IFFT processor 106 assigns each set of data symbols to modulate a set of N subcarrier waves (i.e., OFDM tones), where the number of data symbols in a set is less than or equal to the number N of subcarriers. Assignment is performed such that each data symbol C[k] in a set modulates a different subcarrier k in the set of subcarriers. Furthermore, assignment may be performed using any of a number of methods commonly known in the art, including but not limited to methods such as single-carrier modulation (SCM) and dual-carrier modulation (DCM). Each set of symbol-modulated subcarriers is then IFFT transformed into a time-domain, digital OFDM symbol.
Each time-domain OFDM symbol is then prepared for transmission. First, OFDM transmitter 100 may have cyclic prefix inserter 108, which inserts a cyclic prefix onto each OFDM symbol. Then, the OFDM symbol may be converted to analog format by digital-to-analog converter (DAC) 110. OFDM transmitter 100 might also employ other processing commonly known in the art such as radio-frequency (RF) modulation to prepare the OFDM symbol for transmission. The OFDM symbols are then transmitted over any one of a number of transmission media, including but not limited to airwaves, fiber optics, and coaxial cables.
FIG. 2 shows a simplified block diagram of one possible implementation of a prior-art OFDM receiver 200 which receives the time-domain OFDM symbols generated by transmitter 100 of FIG. 1. Receiver 200 has analog-to-digital converter (ADC) 202 which converts received, time-domain OFDM symbols from analog to digital format. Cyclic prefix remover 204 removes the cyclic prefix from each time-domain OFDM symbol if the transmitter employed cyclic prefix insertion. Fast Fourier transform (FFT) processor 206 converts each time-domain OFDM symbol into a set of frequency-domain received data symbols. Each received data symbol R[k] in a set may be represented as a function of the originally transmitted data symbol C[k], the frequency response H[k] of the tone k, and the noise V[k] with variance σ2 added to the transmitted signal as shown in Equation (1) below:R[k]=H[k]C[k]+V[k].  (1)
Equalizer 208 equalizes each received data symbol R[k] to generate an equalized symbol. Equalization may be performed using any one of a number of approaches commonly known in the art. For example, one such approach is a zero-forcing approach in which each received data symbol R[k] in a set is equalized by dividing the received data symbol R[k] by an estimate H[k] of the frequency response. Assuming a perfect estimation of H[k], the zero-forcing equalized data symbol Y[k] may be represented by Equation (2) as follows:
                                          Y            ⁡                          [              k              ]                                =                                                    R                ⁡                                  [                  k                  ]                                                                              H                  _                                ⁡                                  [                  k                  ]                                                      =                                                            C                  ⁡                                      [                    k                    ]                                                  +                                                      V                    ⁡                                          [                      k                      ]                                                                                                  H                      _                                        ⁡                                          [                      k                      ]                                                                                  =                                                C                  ⁡                                      [                    k                    ]                                                  +                                  U                  ⁡                                      [                    k                    ]                                                                                      ,                            (        2        )            where the noise U[k] has a variance
      σ    U    2    =            1                                                            H              _                        ⁡                          [              k              ]                                                2              ⁢                  σ        2            .      To eliminate the division operation of Equation (2), and thus, reduce the complexity of the equalization process, equalized data symbol D[k] can be computed as shown in Equation (3):D[k]= H*[k]R[k]=| H[k]|2Y[k]=| H[k]|2C[k]+ H*[k]V[k],  (3)where the noise H*[k]V[k] has variance | H[k]|2σ2 
Each equalized data symbol D[k] is then demapped by data symbol demapper 210 using a constellation that corresponds to the mapping used by transmitter 100 of FIG. 1. In so doing, data symbol demapper 210 determines which original data symbol C[k] in the constellation is the likely value (e.g., the likelihood estimate) for the equalized data symbol D[k]. The likelihood estimates may be calculated using any of a number of methods commonly known in the art. For example, demapper 210 may determine the likelihood estimates by calculating log-likelihood ratio (LLR) values through zero-forcing or maximum-likelihood (ML) techniques for the equalized data symbols D[k].
The likelihood estimates are then processed by downstream processing 212. Downstream processing 212 performs operations to recover the originally transmitted bitstream from the likelihood estimates and may include processing such as Viterbi decoding or other processing commonly known in the art to recover the originally transmitted data bitstream.
OFDM Modulation Employing QPSK and SCM
As discussed above, transmitter 100 converts the serial bitstream into digital, time-domain OFDM symbols using OFDM modulation. OFDM modulation may be implemented using different combinations of mapping and subcarrier modulation. For example, in a first such OFDM modulation implementation, data symbol mapper 104 of FIG. 1 employs QPSK mapping, and IFFT processor 106 employs single-carrier modulation.
FIG. 3 graphically illustrates one possible implementation of a constellation that may be used in QPSK mapping. Data symbol mapper 104 divides the serial bitstream into groups of two bits each. Each two-bit group is mapped using the constellation of FIG. 3 to generate a data symbol C[k], which has an in-phase (i.e., real) component CI[k] and a quadrature (i.e., imaginary) component CQ[k]. The in-phase component CI[k] corresponds to the first bit (i.e., b1) of the two-bit group, and the quadrature component CQ[k] corresponds to the second bit (i.e., b2) of the two-bit group.
FIG. 4 graphically illustrates a frequency-domain representation of the assignment of a set of data symbols to a set of OFDM tones using SCM. In this example, the number of data symbols is equal to the number N of tones, and thus, each tone k is assigned a data symbol C[k].
After transmission, demapper 210 of FIG. 2 demaps each equalized data symbol D[k] of each received QPSK, SCM OFDM symbol using the constellation of FIG. 3. Specifically, for each equalized data symbol D[k], demapper 210 estimates the most likely combination of bits given the constellation of FIG. 3.
OFDM Modulation Employing 16-QAM and SCM
In a second OFDM modulation implementation, data symbol mapper 104 employs 16-quadrature amplitude modulation (16-QAM), and IFFT processor 106 employs SCM.
FIG. 5(a) graphically illustrates one possible implementation of a constellation that may be used in 16-QAM mapping. Data symbol mapper 104 divides the serial bitstream into groups of four bits. Each four-bit group is mapped using the constellation of FIG. 5(a) to generate a data symbol C[k], which has a real component CI[k] and an imaginary component CQ[k]. The real component CI[k] corresponds to the first two bits (i.e., bits b1 and b2) of the four-bit group, and the imaginary component CQ[k] corresponds to the third and fourth bits (i.e., bits b3 and b4) of the four-bit group.
IFFT processor 106 then assigns each set of data symbols to a set of N subcarriers using SCM. Assignment is performed in a manner similar to that of the first OFDM modulation implementation discussed above (e.g., as shown in FIG. 4).
After transmission, demapper 210 of FIG. 2 demaps each equalized data symbol D[k] of each received 16-QAM, SCM OFDM symbol using the constellation of FIG. 5(a). Specifically, for each equalized data symbol D[k], demapper 210 estimates the most likely combination of bits given the constellation of FIG. 5(a).
Given the same number N of subcarriers, OFDM modulation implementations employing 16-QAM and SCM are capable of transmitting twice as much data as that of implementations employing QPSK and SCM. Specifically, each data symbol C[k] in a 16-QAM, SCM implementation transmits four bits, while each data symbol C[k] in a QPSK, SCM implementation transmits only two bits. However, demapping of QPSK, SCM implementations is typically more robust against errors than that of 16-QAM, SCM implementations. As shown in FIG. 3 and FIG. 5(a), the constellation points of the 16-QAM constellation are spaced closer together than those of the QPSK constellation. Therefore, in the 16-QAM, SCM implementation, there is a greater chance that one of the equalized data symbols D[k] will be mistaken for an incorrect constellation point. Failure to properly demap the equalized data symbols may result in corrupted data. An error in one demapping may corrupt the entire stream of data, and consequently, the transmission may need to be resent, requiring extra transmission time and computational power.
OFDM Modulation Employing 16-QAM and DCM
In a third OFDM modulation implementation, data symbol mapper 104 employs 16-QAM, and IFFT processor 106 employs dual-carrier modulation. In this case, data symbol mapper 104 generates four-bit groups in a manner similar to that of the second implementation above. However, instead of mapping each group of four bits using one 16-QAM constellation, data symbol mapper 104 maps each group of four bits using two separate 16-QAM constellations. In so doing, data symbol mapper 104 generates two different data symbols for each four-bit group.
FIG. 5 graphically illustrates two possible implementations of constellations that may be used for 16-QAM, DCM mapping. Each four-bit group is mapped using the constellation of FIG. 5(a) to generate data symbol C[k]. Additionally, each four-bit group is mapped using the constellation of FIG. 5(b) to generate corresponding data symbol C[k′]. Note that data symbols C[k] and C[k′] have real components CI[k] and CI[k′], respectively, which correspond to the first two bits (i.e., bits b1 and b2) of the four-bit groups and imaginary components CQ[k] and CQ[k′], respectively, which correspond to the third and fourth bits (i.e., bits b3 and b4) of the four-bit groups.
IFFT processor 106 then assigns each set of N/2 pairs of corresponding data symbols to a set of N subcarriers. Assignment is performed such that the two data symbols in each pair of corresponding data symbols (e.g., C[k] and C[k′]) are assigned to two different subcarriers, spaced apart by a number, preferably N/2, of subcarriers.
FIG. 6 graphically illustrates a frequency-domain representation of the assignment of a set of N/2 pairs of corresponding data symbols to a set of OFDM tones using DCM. In this example, the number of data symbols is equal to the number N of tones, and thus, each tone is assigned a data symbol. Each data symbol C[k] is assigned to a tone k in the first half of the set of tones (i.e., k=1, 2, . . . , N/2), such that data symbols C[k] range from tone 1 to tone N/2. Each corresponding data symbol C[k′] is assigned to a tone k′ in the second half of the set of tones (i.e., k′=N/2+1, N/2+2, . . . , N), such that data symbols C[k′] range from tone N/2+1 to tone N. Furthermore, the two data symbols corresponding to the same four-bit group are separated by a distance of N/2 tones. Thus, tone 1 and tone N/2+1 correspond to the same four-bit group, tone 2 and tone N/2+2 correspond to the same four-bit group, and so forth.
After transmission, demapper 210 of receiver 200 demaps each equalized data symbol D[k] using the constellation of FIG. 5(a) and each equalized data symbol D[k′] using the constellation of FIG. 5(b). If a log-likelihood ratio approach is used, then likelihood estimates are determined for each equalized data symbol. In this case, demapper 210 generates four likelihood estimates for each four-bit group from one equalized data symbol D[k] and four likelihood estimates for the same four-bit group from the corresponding equalized data symbol D[k′]. Downstream processing 212 then performs an additional step of combining the two likelihood estimates that correspond to the same four-bit group. Combining may be performed using any of a number of different methods. For example, in one such method, the likelihood estimates could be weighted based on the power of the channel response estimates H[k] and H[k′] received from equalizer 208 and then the weighted likelihood estimates could added together.
Given the same number N of subcarriers, OFDM modulation implementations employing 16-QAM and DCM are capable of transmitting the same amount of data as implementations employing QPSK and SCM. Specifically, 16-QAM, DCM OFDM implementations transmit four bits on two subcarriers (i.e., an average of 2 bits/subcarrier), while QPSK, SCM OFDM implementations transmit two bits on one subcarrier (i.e., an average of 2 bits/subcarrier). Furthermore, since 16-QAM, DCM OFDM implementations use two data symbols (e.g., C[k] and C[k′]) for each group of four bits, receiver 200 has two opportunities to recover each bit in a four-bit group. Thus, if one data symbol is corrupted, then the four-bit data group may be recovered from the other data symbol corresponding to the same four-bit group. For this reason, 16-QAM, DCM implementations are more robust against some kinds of data corruption, such as errors caused by frequency selective fading, than QPSK SCM and 16-QAM SCM implementations. However, the method of demodulating each equalized data symbol separately and combining corresponding likelihood estimates downstream does not fully exploit the frequency-diversity advantages gained by employing DCM.